Equations and formulae

1. If n is an even integer, which expression represents the product of n and the next consecutive even integer?

1. n(n + 1)
2. 2n(n + 1)
3. n(n + 2)
4. n^2 + 2

2. A rectangle has width x cm, length x + 4 cm and perimeter 36 cm. Which equation models the perimeter?

1. x(x + 4) = 36
2. 2x + 2(x + 4) = 36
3. x + 2(x + 4) = 36
4. 4x + 4 = 36

3. Solve 7x - 5 = 30.

1. x = 25/7
2. x = 5
3. x = 35
4. x = -5

4. Solve 5 - 2x = 3(x + 7).

1. x = -16/5
2. x = 16/5
3. x = -26
4. x = -8/5

5. Solve x/3 - (x - 2)/4 = 5.

1. x = 6
2. x = 18
3. x = 54
4. x = 66

6. Solve x/(2x + 1) = 4.

1. x = 4/7
2. x = -4/7
3. x = -1/2
4. x = 4

7. Solve x/(x + 2) = 3/(x - 6).

1. x = (9 ± √105)/2
2. x = (9 ± √57)/2
3. x = 3 or x = -2
4. x = 6 only

8. Solve 2/(x + 2) + 3/(2x - 1) = 1.

1. x = 3 or x = -1
2. x = 2 or x = -3
3. x = -2 or x = 1/2
4. x = 1 or x = -3

9. Before solving 4/(x - 5) = x, which restriction must be recorded?

1. x ≠ 0
2. x ≠ 4
3. x ≠ 5
4. x > 5

10. Solve 2x + 3y = 17 and 3x - 2y = 6.

1. x = 3, y = 4
2. x = 4, y = 3
3. x = 5, y = 2
4. x = 2, y = 5

11. Solve y = 2x - 1 and 3x + y = 19.

1. x = 4, y = 7
2. x = 5, y = 9
3. x = 3, y = 5
4. x = 4, y = 9

12. Three adult tickets and two child tickets cost $34. Two adult tickets and five child tickets cost $41. What are the ticket prices?

1. Adult $7, child $6.50
2. Adult $8, child $5
3. Adult $9, child $3.50
4. Adult $6, child $8

13. Solve x^2 - 9x + 20 = 0.

1. x = -4 or -5
2. x = 2 or 10
3. x = 4 or 5
4. x = -2 or -10

14. Solve 2x^2 - 5x - 3 = 0.

1. x = -3 or 1/2
2. x = 3 or -1/2
3. x = -3 or -1/2
4. x = 3 or 1/2

15. Use completing the square to solve x^2 - 6x - 7 = 0.

1. x = 3 ± √7
2. x = 7 or -1
3. x = 3 or -3
4. x = 6 or 1

16. Write 2x^2 + 8x - 3 in completed-square form.

1. 2(x + 2)^2 - 11
2. 2(x + 4)^2 - 35
3. 2(x + 2)^2 - 3
4. (2x + 4)^2 - 19

17. Solve 3x^2 + 2x - 4 = 0 exactly.

1. x = (-1 ± √13)/3
2. x = (-2 ± √13)/3
3. x = (1 ± √13)/3
4. x = (-1 ± √3)/3

18. Solve x^2 + 4x + 1 = 0 exactly.

1. x = -2 ± √3
2. x = 2 ± √3
3. x = -4 ± √15
4. x = -2 ± √5

19. A rectangle has width x cm, length x + 3 cm and area 40 cm^2. What is its width?

1. 4 cm
2. 5 cm
3. 8 cm
4. -8 cm

20. Make t the subject of v = u + at, where a ≠ 0.

1. t = (v - u)/a
2. t = a/(v - u)
3. t = (u - v)/a
4. t = v - u/a

21. Make x the subject of y = (3x - 5)/2.

1. x = (2y - 5)/3
2. x = (2y + 5)/3
3. x = 2(y + 5)/3
4. x = (y + 10)/3

22. Make x the subject of P = (ax + b)/(cx + d), assuming Pc - a ≠ 0 and the original denominator is non-zero.

1. x = (Pd - b)/(a + Pc)
2. x = (b - Pd)/(Pc - a)
3. x = (b + Pd)/(Pc + a)
4. x = (Pd - b)/(Pc + a)

23. Make r the subject of A = πr^2, where r is a radius.

1. r = A/π
2. r = √(A/π)
3. r = π√A
4. r = A^2/π

24. Make L the subject of T = 2π√(L/g), where g > 0 and T ≥ 0.

1. L = gT^2/(4π^2)
2. L = 4π^2g/T^2
3. L = gT/(2π)
4. L = T^2/(4π^2g)