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1 of 5 Topic test Algebra and equations • Time allowed: 45 minutes • Calculators are not allowed. • Part A: 20 multiple-choice questions (40 marks) • Part B: 10 free-response questions (60 marks) Name: _________________________________________ 7 Which expression is equal to 6p – p? A 6p2 B –5p C 5p D 6 8 Which expression is equal to 10ab2? Part A 20 multiple-choice questions 2 marks each: 40 marks Circle the correct answer. A 100ab2 B 10 × a × b × b C 10 × a × a × b × b D 10ab × 10ab 1 Which expression is equal to w × w × w? 9 Solve 2y + 1 = 8. A 3+w B 3w D w3 C w+3 A y = 3.5 B y=3 C y=4 D y = 4.5 2 Which expression is equal to 3 × u × u × 10? 10 If a = 4, what is the value of 3a + 4? A 30u2 B 60u2 C 13u2 D 60u A 11 B 38 C 16 D 18 3 Which expression is equal to 17 × 12? 11 Which expression represents the quotient of x and 5? A 17 + 10 × 17 + 2 B 17 × 10 + 17 × 2 C 17 × 10 + 2 D 17 × 10 × 2 4 Which equation is false? B a × a = a2 C a×b=b×a D a+b=b+a 5 If x represents any number, which expression represents C 5x D x 5 B –1 A 0 C 1 D 1k 13 Callum solved the equation 2a – 5 = 19 incorrectly, like this: 3 less than that number? B 3x – 3 B x 5 12 Which of the following is equal to k – k? A a÷b=b÷a x A 3 A x5 2a – 5 19 C 3–x D x–3 2a 19 – 5 Line 1 2a 14 Line 2 14 2 a 7 a 6 Solve x 19 28 . Line 3 Line 4 In which line did Callum first make a mistake? A x=8 B x = 47 C x=9 D x = 48 A Line 1 B Line 2 C Line 3 © Cengage Learning Australia Pty Ltd 2011 MAT07NATT10005 www.nelsonnet.com.au Number and Algebra: Patterns and algebra, Linear and non-linear relationships D Line 4 2 of 5 14 If c = –6, find the value of 4c – 10. B –34 A 12 C –12 b 30 × 70 D –20 c 25 × 9 15 Which is the correct formula for the perimeter (P) of a rectangle with length l and width w? A P=l+w B P = lw C P = 2l + 2w D P = 4lw 22 (2 marks) Examine this number pattern, then write a general rule for it using a variable. 9 ÷ (–9) = –1 4 ÷ (–4) = –1 16 Which one expression is not equal to the other three? A 0÷a 17 Solve B 0+a C a–a D 0×a x 8 20 . 3 A x = –4 7 ÷ (–7) = –1 1 ÷ (–1) = –1 23 (6 marks) If p represents any whole number, write an algebraic expression for: B x = 12 C x=4 D x = 36 18 If C = 3m – 4, what is the value of C when m = 7? A C=9 10 ÷ (–10) = –1 B C=6 C C = 17 a the number multiplied by itself b the difference between the number and 4 D C = 33 c the next consecutive whole number 19 Which one of the following expressions is not equal to 2p? A p2 B p×2 C p+p D 4p – 2p 24 (10 marks) Simplify each expression. a 3×b÷4 20 If f = 3 and g = –1, which of the following is equal to f 2 + g2? A 5 B 8 C 10 D 7 Part B 10 free-response questions 60 marks Show working where appropriate. b h×h–2×d c r×9+r×r d 4m + 4m + 4m 21 (6 marks) Evaluate each expression. a 2 × 18 × 5 e 18 × p ÷ (z + 1) © Cengage Learning Australia Pty Ltd 2011 MAT07NATT10005 www.nelsonnet.com.au Number and Algebra: Patterns and algebra, Linear and non-linear relationships 3 of 5 25 (12 marks) If a = 6, b = 12 and c = –3, evaluate: b how many times 5 divides into q a a+c c 10 more than triple b b 10 – b d 5 less than half of g c 12 c 28 (8 marks) Solve each equation. d 2c + 9 e 2bc a k 21 3 b d –6=2 4 f 5a – b c 4m + 8 = 36 26 (2 marks) Use the guess-and-check method to find the solution to the equation 8p – 5 = 19. Show all working. d 2n 2 3 27 (8 marks) Write an algebraic expression for: a n decreased by 2 © Cengage Learning Australia Pty Ltd 2011 MAT07NATT10005 www.nelsonnet.com.au Number and Algebra: Patterns and algebra, Linear and non-linear relationships 4 of 5 29 (2 marks) The number of hours of sleep recommended A for children has the formula H = 14 – , where H is 2 the number of hours and A is the age of the child in years. Use the formula to find the number of hours of sleep recommended for a 6-year-old child. 30 (4 marks) If you divide Alex’s age by 3 and subtract 2, you get his daughter Ellen’s age, 9. a Write an equation to find a, Alex’s age. b Solve the equation from part a to find Alex’s age. This is the end of the test. Use the back for extra working space. © Cengage Learning Australia Pty Ltd 2011 MAT07NATT10005 www.nelsonnet.com.au Number and Algebra: Patterns and algebra, Linear and non-linear relationships 5 of 5 Answers Part A 1 D 9 A 17 D 2 A 10 C 18 C 3 B 11 D 19 A 4 A 12 A 20 C 5 D 13 A 6 C 14 B 7 C 15 C 8 B 16 B Part B 21 a 180 b 2100 c 225 22 n n 1 (other variables possible) 23 a p2 b p–4 c p+1 3b 24 a 4 b h 2d c 9r r 2 d 12m e 25 a 3 26 p = 3 b –2 c –4 d 3 e –72 27 a n 2 b c 3b 10 d 2 q 5 18 p z 1 f 18 g 5 2 28 a k = 63 b d = 32 c m=7 d n = –3 29 H = 11, the number of hours required is 11 hours. 30 a a 2 9 3 b Alex is 33 © Cengage Learning Australia Pty Ltd 2011 MAT07NATT10005 www.nelsonnet.com.au Number and Algebra: Patterns and algebra, Linear and non-linear relationships