The equation of the straight line that passes through the point (-4, 6) and is perpendicular to the line y+2x-3=0 is

4y-2x+7=0

y+2x+2=0

y-2x-14=0

2y-x-16=0

2y+x-8=0

If 1/a = 1/b + 1/c and a and c are both doubled, the value of b will be

divided by 4

divided by 2

unchanged

multiplied by 2

multiplied by 4

Let b be a real number such that b²=b³+1. Which of the following is false?

b³-b⁴=b

b²=b⁴+b+1

b⁴+b³+b²=1

b³+b+1=b³+b²+1+1/b

b³+b²+1=2b³+2

For which values of k does the equation x²+kx+1=0 have at least one real root?

k ≥ 2

k ≤ -2

k ≤ 2

k ≤ -2 or k ≥ 2

-2 ≤ k ≤ 2 

If x = 2log_t(t²) + log_(t³)(5) then t^x =

t⁴(5)^1/3

t⁴ + (5)^1/3

  t⁴+(log_t5)/3

(t⁴log_t5)/3

None of A to D is correct

If (1-2x²)^−3/2 + 6x²(1-2x²)^−5/2 is written as a single fraction in the form (1+Ax²)/(1-2x²)^5/2 then the value of the constant A is

4

6

8

12

16

A box containing three bags of sugar weighs 6.0 kg. When the same box contains five bags of sugar it weighs 9.2 kg. How heavy is the empty box?

1.2 kg

1.6 kg

2.0 kg

3.2 kg

Can't be sure

If x⁹+512=(x+2)(a₈x⁸+a₇x⁷+...+a₁x+a₀) then what is the value of a₈+a₇+...+a₁+a₀?

1

19

57

17

171

The symbol 25! denotes the product of all the whole numbers from 1 up to 25. If the actual value of 25! is calculated, how many zeros will be at the end?

1

3

4

5

6

A product in a shop is reduced in price by 20%. At this reduced price the shopkeeper makes only 4% profit. What percentage profit (to the nearest whole percent) does the shopkeeper make at its normal selling price?

16

24

25

30

84

A boy walks at 4 km per hour and runs at 6 km per hour.

If he runs to school instead of walking, then he saves 3 minutes and 45 seconds.

How far does he live from school?

0.125 km

0.375 km

0.75 km

6.9 km

7.5 km

The values of x satisfying 2x³+5x²-3x > 0 are

x < -3 or x > 1/2

x < -3 or 0 < x < 1/2

-3 < x < 1/2

-3 < x < 0 or x > 1/2

x > 1/2

The expression (1 + sinθ + cosθ)² is the same as 

2(1 + sinθ)(1 + cosθ)

4 + sin(2θ)

(1 + sin(2θ))(1 + cosθ) 

4

2 + sin(2θ)

How many values of θ in the range 0 ≤ θ ≤ 2π satisfy the equation 2cos²θ - sinθ = 1 ? 

 4

3

2

1

0

In the diagram below there are two squares. The smaller square has sides of length x. The larger square has sides of length x+y.

The area of the small square is one third of the area of the large square.

What is the value of x/y ?

(3^1/2 + 1)/2

1/(3)^1/2

1/9

3^1/2

3^1/2 − 1

Let cot(θ)=a.

What is the value of cot(θ)+cot(2θ)?

(3a²-1)/(2a)

(1+3a²)/(2a)

(a²+2a -1)/(2a)

(a+1)²/(2a)

(a²+1)/(2a)

If a is a constant and 4^x −5(2^x) = a is true for at least one real number x then what can be concluded about the number a?

a ≥ -25/2

a ≥ -25/4

a ≤ -25/2

a ≤ -25/4

-25/2 ≤ a ≤ 25/4

Let y=(0.2x)/(x+1). If x takes all values in the range [1,∞) then what range of values does y take?

[0.1, 0.2)

(0, 0.1]

(0, 0.2)

[0, 0.1]

[0.1, 0.2]

Let arctan(x) denote the inverse function of tan(x).

Simplifying the expression tan(arctan(α) + arctan(1-α)) produces

1/(1+α+α²)

1/(1-α-α²)

1/(α²-α+1)

1/(α²-α-1)

1/(α²+α)

A square has centre (2,1). One vertex is at (5,6). Points P, Q, R have coordinates P := (−3, 4), Q := (−1, −4) and R := (5, −4). Which of the following are vertices of the square?

P, Q and R

P only

P and R only

Q only

P and Q only

In the diagram below, AB, EF and DC are perpendicular to BC. AEC and BED are straight lines. AB = x, EF = h and DC = y. Then h is:

xy/(x + y)

(x² + y²)/(2x + 2y)

(x³ + y³⁾/4xy

(x + y)/xy

Not enough information is provided to solve the problem

The number of prime values of the polynomial n³ − 10n² − 84n + 840 where n is an integer is

0

1

2

4

infinite

If (2²ⁿ⁺⁴- 4ⁿ)/30 is simplified, the answer is

2²ⁿ⁺²

2ⁿ⁺²

2^n-2

2²ⁿ⁺¹

2^2n-1

If a>1 and a^x − a^x −2 = 19, then what is the value of x?

log_a(1+365^0.5)-log_a(2)

log_a(a²+19)-log_a(365^0.5)

log_a(a²-1)-log_a(19)-2

log_a(a-1)-log_a(19)-2

log_a(19)+2-log_a(a²-1)

Let d(x)=cos⁴x −sin⁴x

How many of the functions below are equal to d(x) for all x∈(0,π/2)?

e(x) = cos(2x)

f(x) = 1 − 2sin²x

g(x) = (cosx + sinx)(cosx − sinx)

h(x) = (1 − sinx)(1 + tanx)(1 + sinx)(1 − tanx)

0

1

2

3

4

A regular hexagon ABCDEF has sides of length 2 cm. M is the midpoint of AB. Which of the following line segments have length 13^1/2 cm?

BD

BE

EM

FM

None of these

If the number n is a perfect square, what is the next perfect square above it?

n + n^1/2

n + 2(n)^1/2 + 1

n² + 1

n² + n

n² + 2n + 1

The domain of the function f(x) =log₃(3-x)+ ∛(3x+1) is 

[Definition: The domain of a function is the set of x values for which the function is defined.]

x ≥ -1/3

-1/3 ≤ x < 3

x < 3

x ≤ -1/3

x > 3

If we make x the subject of the equation y = (3x-1)/(x+2) then we get

x = (-1-2y)/(y+3)

x = (1+2y)/(3-y)

x = (y+2)/(y-3)

x = (1+2y)/(y-3)

x = (-1-2y)/(2y+3)

A driver travels an average of k miles a day for the first d days of a journey and then m miles a day for the next b days. The car uses x litres of petrol per 100 miles. How many litres of petrol does the car use for the whole journey ?

x(kd + mb)/100

(k + m)x/100

100(k + m)/x

100(kd + mb)/x

bdkmx/100