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1. Non Calculator Tests Third Year

2. Click on a number in the table above to go to the test of your choice. The solutions follow after the test

3. Non Calculator – Test 1 1. What is (7)  (8) ? 2. Express 19/20 as a decimal 3. What is 121 ? 4. Express 186 000 in scientific notation (standard form) 5. List all the factors of 18 6. What is the product of 20 and 300 ? 7. Find 5·2  4 8. Round 1874 to 2 significant figures 9. A boy scored 16 out of 20 in a test. Express this as a percentage. 10. What is ?

4. Non Calculator – Test 2 • 1. Split £20 between 2 people in the ratio 4 : 1. • How much does each receive ? • 2. Simplify 8x  2 + 3x + 10 • 3. Simplify 2a  5a  3b • 4. At a speed of 30 km/hr, how far would I travel in hours ? • 5. What is 43 ? • 6. What is 6·8 + 0·24 ? • 7. Round 3·508 to 2 decimal places. • 8. Find the area of a rhombus with • diagonals 10 cm and 7 cm • 9. What is the median score for these test results : • 12, 13, 18, 12, 10 ? • When a dice is rolled, what is the • probability of a 5 appearing ?

5. Non Calculator – Test 3 • 1. Factorise 2x2  6x fully • 2. What is 1/2  4/5 simplified as far as possible ? • 3. Find 6  (  8) • Express 34/5 as a decimal • 5. Express 0·0064 in scientific notation (standard form) • What are the quotient and remainder when 30 • is divided by 7 ? • What is 0·2  0·4 ? • 3 buns cost 48 pence. What will 2 buns cost ? • Remove the brackets 3x(2x  4) • The scale on a map is 1 : 5000. • On the map, a field is 4 cm long. • What is the real length of the field in metres ?

6. Non Calculator – Test 4 • 1. Express 0·05 as a fraction in its simplest form • 2. What is 75% of £160 ? • What is the value of 2a2 when a = 3 ? • 4. Write down all the whole numbers satisfying the inequality • 2x + 1  7 • The diameter of a circle is 6 cm. • Which of these is an approximate answer for its circumference ? • 14 cm, 19 cm, 24 cm, 30 cm ? • 6. What are the prime factors of 20 ? • Round 12·076 to 3 significant figures • This figure consists of 2 parallel lines and an isosceles triangle. Find x • 9. When a spinner is spun, what is the probability of it stopping • on an even number ? • 10. 2 men can build a wall in 6 days. • How long, at the same rate, would 3 men take ?

7. Non Calculator – Test 5 • 1. What is (18)  (3) ? • 2. What is 400 ? • A number in scientific notation is 2·13  104. • Write out the number in full. • 4. Evaluate 2·0  0·15 • 5. I bought a C.D. player for £40 and sold it for £30 making a £10 loss. • Express this loss as a percentage of the cost price of £40. • 6. Simplify 8y + 3w  y + 4w • 7. Write down the formula for calculating the area of a circle. • 8. Here are the ages of a group of boys : • 10, 12, 14, 12, 12, 13, 15, 12, 10, 10 • What is the modal age (the mode) ? • 9. If 5x + 6 = 4x + 10, what is the value of x ? • 10. A model car is 20 cm long. • On a scale drawing, the car in the picture is 5 cm long. • What is the scale factor ?

8. Non Calculator – Test 6 1. Express 1/3 as a decimal 2. Which of the following is NOT a factor of 24 : 1, 2, 3, 4, 5, 6, 8 ? 3. What is 7  0·04 ? 4. How many 1/8 ’s are there in 1/2 ? 5. Share £15 between 2 people in the ratio 2 : 1 How much does each person receive ? 6. Simplify 5x  3y  y 7. It is 50 km from my house to the airport. How long would it take me to get there at an average speed of 20 km/hr ? 8. Write down a relationship between the 3 sides of this right angled triangle. 9. What is the probability of choosing a square from this board which contains a cross ? 10. Find 12  2  5

9. Non Calculator – Test 7 • 1. What is the value of 34 (3 to the power 4) ? • 2. Find half of 9·9 • Round 68·975 to 3 significant figures. • Find % of £18 • 5. To pack 4 boxes full of tins takes 20 minutes. • How long would it take to pack 3 boxes ? • 6. Factorise 6xy  9x • Evaluate 20  2p2 when p = 3 • Calculate the area of this kite • 9. Express £2 as a percentage of £5 • 10. There are 2 parallel lines in this figure. • Calculate the size of the angle marked x.

10. Non Calculator – Test 8 • 1. If x = -2 find the value of 8 – 3x • 2. What is the value of (52 + 122)? • Write 28000 in scientific notation. • 4. Find the size of the acute angle between the hands of a clock at 4.30pm • 5. Find 17½% of £800 • 6. I have just received a 50% pay rise and now earn £60000 pa. • How much did I earn before the pay rise? • 7. Simplify the expression (x+1)2 – x(x+2) • 8. What is the value of 0.53 • Evaluate ½ of ½ + ½ • A rectangle has a length 4 and a breadth x. • The area of the rectangle is 50cm2. • Find the breadth of the rectangle.

11. Non calculator – Test 9 1. Express as a decimal 2. What is the value of 32 + 42 ? 3. What is the product of 4, 3, 2, 1 and 0 ? 4. Round 375 001 to 2 significant figures 5. George scored 36/50 in a test. What was George’s percentage mark ? 6. Evaluate 1/2  2/3  3/4  4/5 7. A man owns 80 hectares of land. He divides it between his 2 sons in the ratio 1 : 3. How many hectares does each son receive ? 8. Simplify 3x2 + 4x + 2x2 6x 9. Calculate the area of this triangle. 10. What is the value of 24  (8) ?

12. Non Calculator – Test 10 • 1. What is  5  4 ? • 2. Express 0·038 in standard form (scientific notation) • 3. Find 1·1  0·75 • 4. I have a certain fixed amount of money. • I can buy 3 books at £8 each. • How many books could I buy if they had cost £6 each ? • 5. Simplify 4a  7a • Factorise 12a  8b • 7. I reduce this large picture to • the small one in a photograph. • What is the scale factor ? • 8. Calculate the size of the • angle marked x in this figure. • 9. The mean age of 2 boys, David and John, is 13. • David is 10. How old is John ? • When a normal dice (die) is rolled, • what is the probability that it will land showing an even number ?

13. t p v Non Calculator – Test 11 1. Express 15/4 as a decimal 2. Which of the following is not a prime factor of 30 : 2, 3, 5, 7 ? 3. Find 0·72  6 4. What is 331/3 % of £210 ? 5. Expand the brackets 3a(5a  2b) 6. The circumference of a circle is 31 cm. Which of these is most likely to give the size of the diameter ? 5 cm, 10 cm, 15 cm, 20 cm ? 7. Express £9 as a percentage of £12 8. Simplify 7a  2b  a + 5b 9. What is the value of 3 cubed plus 3 ? 10 Which of these is not true for the triangle shown t2 = p2 + v2 , v2 = t2 p2 , p2 = t2  v2 , v2 = t2 + p2

14. Non Calculator – Test 12 1. What is (45)  (5) ? 2. Express 0·000052 in scientific notation (standard form) 3. The product of two numbers is 36. One of them is 9. What is the other one ? 4. What is 2  0·95 ? 5. Express 0·096 to two decimal places 6. What is 17/8 + 1/4 ? 7. What is the value of ab2 given that a = 5 and b = 2 ? 8. A tortoise moves at 12 centimetres per minute. How far will it travel in 5 minutes ? 9. Calculate the areaof this parallelogram 10. Solve for x, 2x  1 = x + 4

15. 5.2

16. Non Calculator – Test 13 • 1. What is 79  (  21) ? • 2. The scale of a map is 1 : 10 000. A line on the map is 3 cm long. • What length does this really represent (in metres) ? • 3. Write down all the factors of 21 • 4. In a small test, Scott scored 4 out of 5. • What was his percentage mark ? • A piece of string is 24 cm long. It is cut into 2 pieces whose lengths are in the ratio 5 : 1. • What length is each piece ? • 6. Simplify (3p)2  q • 7. What is 0·24 as a fraction in its simplest form ? 8. Factorise 15n2 30n 9. ABCD is a parallelogram. What is the size of the angle marked x ? 10. Look at these test results. 13, 14, 14, 14, 16, 16, 17, 18, 20 What is the larger  the median or the mode ?

17. Non Calculator – Test 14 1. What is 302 ? 2. What quotient and remainder do you get when you divide 30 by 7 ? 3. Simplify 5a(2a + 4) 4. Round 13 689 to 3 significant figures 5. How may 1/2’s in 41/2 ? 6. Out of 20 people at a meeting, 4 wore glasses. What percentage of the group wore glasses ? 7. To walk 5 km took Laura 40 minutes. How long, at the same speed, did it take her to walk 3 km ? 8. Simplify 10p + 3q  p  5q 9. What is 0·2  0·3 ? 10. Which of these are NOT solutions of x + 4 < 10 5, 6, 4, 3, 1 ?

18. 20cm 12cm t w a Non Calculator – Test 15 1. What is (6)2 ? 2. Express 2 4/5 as a decimal ? 3. Write out 2·3  104 as a decimal 4. Write down all the multiples of 6 between 40 and 50 5. What is 1·4 + 0·65 ? 6. Find the value of 100  3t when t = 25 7. Find 5·2  4 8. The diagonals of a rhombus are 20 cm and 12 cm. Calculate its area. 9. Write down a connection between the lengths of the three sides of this triangle. 10. If a card is chosen at random from a pack of cards, what is the probability it will be a spade ?

19. 2 cm Non Calculator – Test 16 1. What is 2. What is the sum of 2, 3, 4, 5 and 6 ? 3. What is 0·54  6 ? 4. In a large test, Brian scored 170 out of 200. What was his percentage mark ? 5. Find 2/3 3/5 6. The ratio of boys to girls passing an exam is 2 : 3 If 12 boys passed, how many girls also passed ? 7. Simplify 2a  3a  4a • 8. Factorise fully 8m  12n • 9. The radius of a circle is 2 cm. • Give an estimate of the length of its circumference. • The mean age of Mrs Jones’s three children is 5. • Tom is 3 and Lucy is 4. • How old is Andrew, the third child ?

20. Non calculator – Test 17 1. Find 2  (3) 2. This number appeared on a calculator display 3.61 04 Write it out in full (not in scientific notation). 3. What is 0·32  0·29 ? 4. Round 0·0648 to 2 significant figures 5. Of 1000 plastic buckets produced in a factory, 80 were faulty. What percentage of buckets were faulty ? 6. At a speed of 3 miles per hour, it took me 4 hours to walk round the isle of Millport. How long would it have taken if I walk at 2 miles per hour ? 7. Simplify 8a + 3b  a  7b 8. The scale of a map is 1 cm = 20 metres. A road is 31/2 cm long on the map. What is its true length ? 9. Calculate the size of the angle between 2 adjacent sides of a regular hexagon. 10. Simplify 4(3t  2)

21. Non Calculator – Test 18 1. What is 7/25 expressed as a decimal ? 2. What is 12 + 22 + 32 ? 3. Give any one common factor of 18 and 30. (except 1) 4. What is 1/2 of 0·9 ? 5. What is 31/4  23/4 ? 6. Simplify 4p  3q  r 7. The range of scores in a test is 15. Paul got the lowest mark of 4. Colin got the highest mark. What was his score ? 8. What is the value of 3p2 when p = 2 ? 9. The diagonals of a kite are 7 cm and 4 cm. Calculate the area of this kite. 10. If a dart lands on this special dartboard, what is the probability it lands on number 5 ?

22. Non Calculator – Test 19 • 1. What is 8 + (5) ? • 2. Express 4 million in scientific notation (standard form) • When a number is divided by 3, the quotient is 4 • and the remainder is 2.What is the number ? • 4. What is 1  0·99 ? • 5. Find 90% of £90 • 6. A man and a woman split their restaurant bill in the ratio 2 : 1. • If the bill was £24, how much did the man pay ? • 7. Factorise x2  x • 8. A boy cycles at an average speed of 20 miles per hour. • How long will it take him to cycle 70 miles ? (answer in hours and minutes) 9. The time is half past two. What is the size of the smaller angle between the hands of the clock ? 10. Find x given that 3x + 1 = 2x + 4

23. 4

24. Non Calculator – Test 20 1. Express 31/5 as a decimal 2. What is 14 ? 3. List all the factors of 23 4. Find 5·1 3 5. Round 1 876 000 to 2 significant figures 6. Express £6 as a percentage of £8 7. Simplify 2a + 7b 3a + b 8. What is the largest whole number which is the solution of x + 3 < 11 ? 9. What is the median of these numbers ? 3, 7, 9, 14 10. Simplify 2a(a 3b)

25. 7 x + 5 x 8 Non Calculator- Test 21 • 1. If x = -3 , y = -5 and t = 7 , find the value of 2xy – yt • 2. If x + y = 15 and x – y = 8 , find the value of x. • 3. Find 8% of £386 • 4. Remove the brackets (2x + 1)(x2 – 3x + 5). • 5. Evaluate 13.8 – 14.7 + 4.6 • 6. If 12½% of a sum of money is £18 , find the sum of money. • The perimeter of the rectangle shown is 73cm. • Find the value of x. • 8. The area of the rectangle shown is 92cm2 , find the value of x. • Evaluate ½ of ( 12¼ - 5¾ ) • 10. If sinx = , find the exact value of cosx.

26. 25 x 24 x 3 4 Non Calculator- Test 22 • 1. If x = 3, y = 4 and t = -2 , find the value of • If 2x + y = 23 and y = x + 8, find the value of x. • Find of £210 • 4. Remove the brackets (2x + 1)(x – 1)(x + 2). • 5. Which of these fractions is largest , or • 6. Use Pythagoras to find the value of x in the triangle shown. • 7. Evaluate 3.8 + 6.2 × 5 • 8. Factorize fully x2 – 7x – 18 • 9. Evaluate • 10. If tan x = , find the exact value of sin x.

27. 5 2x + 1 y = x + 1 y P x + y = 8 x Non Calculator- Test 23 • 1. Remove the brackets (x + 4)(x2 – 2x – 5). • If ¾ of a sum of money is £396, find the sum of money. • Find the value of x if 3x + 4y = 7 and x – y = 0. • 4. The area of the rectangle shown is 60 cm2. • Make an equation and find x correct to 1 decimal place. • 5. If x = -1, y = -6 and t = 10 find the value of y2 – 4xt. • 6. Find 40% of £2500. • 7. Factorize fully x3 – 4x • Solve the equation x(x + 8) = (x+2)(x+5) • 9. Find the amount of V.A.T. to be paid on an article costing £400. • ( The rate of VAT is 17½%) • 10. The diagram shows the lines x + y = 8 and y = x + 1. • The lines intersect at the point P. • Find the coordinates of point P.

28. 15 x 12 Non Calculator- Test 24 • 1. If y = -4, find the value of 40 – 5y2. • 2. If y = 2x and x + y = 60 find the value of y. • Factorize fully 9x2 – 121 • 4. Solve the equation x2 =(x+2)(x+1) • Find ¼ of (13¼ - 4¾) • 6. The area of a rectangle is 162cm2. • The length of the rectangle is twice the breadth. • Find the length of the rectangle. • 7. Find x in the triangle shown. • Remove the brackets (2x – 5)(x2 + 4x – 3) • If x is an acute angle and sin x = , find the exact value of tan x. • 10. Can a triangle with sides of length 15 , 21 and 26 be right angled ? • If not, why not?