CSEC Additional Mathematics Paper 1 May/June 2022 - Free CXC Past Paper with Answers

The expression x - 2 is a factor of

$2x^3 + 2x^2 - 4x - 8$

$3x^4 - 10x^3 - 5x^2 + 4$

$\frac{1}{x+3} + \frac{3}{x^2-9}$ expressed as a single fraction is

Which of the following graphs represents $f(x) = x(2+x)$ ?

If $x^2 - 6x + 13 = a(x+h)^2 + k$ , then

$a=1 \quad h=-3 \quad k=4$

$a=1 \quad h=3 \quad k=4$

The number of visas, V(x), issued by an embassy annually is given by $V(x) = 7x^2 - 42x + 72$ . The LEAST number of visas issued in a particular year, x, is

The roots of the equation $5x^2 + 6x - 2 = 0$ are

not real and not equal

not real and not distinct

The values of $x$ for which $\frac{3x-2}{2x+1} \le 0$ are

$-\frac{1}{2} < x \le \frac{2}{3}$

$x \le -\frac{1}{2}$ or $x \ge \frac{2}{3}$

The range of values of $x$ for which $4x - 3x^2 > 0$ is

$\frac{4}{3} < x < 0$

$x < 0, x > \frac{4}{3}$

$0 < x < \frac{4}{3}$

$x > 0, x > \frac{4}{3}$

The expression $\frac{\sqrt{5}-1}{1+\sqrt{5}}$ when simplified is equal to

$\frac{1}{3}(3-\sqrt{5})$

$\sqrt[n]{3 \times 27^m}$ is equal to

The value of $2^z$ where $z = 5 + \log_2 3$ is

Which of the following mathematical statements are true? I. $\log_a PQ = \log_a P \times \log_a Q$ II. $\log_a \frac{P}{Q} = \log_a P - \log_a Q$ III. $\log_a P^b = b \log_a P$

The sum of the first $n$ terms of a series is given by $\sum_{r=1}^{n} (5-3r)$ . The sum of the first 10 terms is

The sum of the first $n$ terms of a geometric series is $S_n = 4^n - 1$ . For this series, I. the common ratio is $-1$ II. the first 3 terms are 3, 12 and 48 III. $S_{2n} = 2^{4n} - 1$

A sequence of positive integers, $\{U_n\}$ , is defined by $U_n = 3\left(\frac{1}{2}\right)^{n-1}$ . The 10th term of the sequence is given by

$-\frac{19683}{512}$

The lines $7x - 4y + 25 = 0$ and $3x - y - 5 = 0$ intersect at the point P. The coordinates of P are

The coordinates of the centre of a circle with equation $(x-1)^2 + (y+3)^2 = 36$ is

The points of intersection of the line with equation $y - x - 2 = 0$ and the circle with equation $x^2 + y^2 = 10$ are

$(3, 1)$ and $(-1, -3)$

The vectors i and j represent 1 km/h east and 1 km/h north respectively. A man sails a boat on a lake such that the velocity is i + 2j when there is no current. If a current of 3i is encountered, then the resulting velocity, v, is

The vector a is given as 5i + 12j. A unit vector parallel to a is

$\frac{1}{13}(5i + 12j)$

$\frac{3}{13}(5i + 12j)$

The position vectors of A and B relative to an origin O are $\begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\begin{pmatrix} 3 \\ -1 \end{pmatrix}$ respectively. The acute angle AOB is given by

$\cos^{-1}\left(\frac{1}{\sqrt{290}}\right)$

Which of the following graphs represents $y = \sin x$ ?

The EXACT value of $\cos\left(\frac{5\pi}{12}\right)$ =

$\frac{1}{4}(\sqrt{6}-\sqrt{2})$

$\frac{1}{4}(\sqrt{6}+\sqrt{2})$

$\frac{1}{2}(\sqrt{6}+\sqrt{2})$

$\frac{1}{2}(\sqrt{6}-\sqrt{2})$

For $0^\circ < x < 360^\circ$ , the equation $3 \sin^2 x = 8 \cos x$ has only one real solution given by

$\sin x = \frac{1}{3}$

$\cos x = \frac{1}{3}$

If $\sin (x+20^\circ)=\cos x$ , then a possible value of x is

$\cos (A + B) + \cos (A - B) = $

The trigonometrical expression $\frac{\sin x}{1 - \cos x} + \frac{\sin x}{1 + \cos x}$ is identical to

The figure MON below shows a quarter circle with radius 4 cm. The perimeter of the figure, in cm, is

The size of angle x, measured in radians, is

The smallest positive angle in radians, within the range $0 \le \theta \le 2\pi$ that satisfies the equation $(2 \cos \theta - 1)(\cos \theta - 2) = 0$ , is

Given that $y = \sqrt{5-x}$ , then $\frac{dy}{dx}$ is

$-\frac{1}{\sqrt{5-x}}$

At the 10 m stopping point on a runway, an airplane is stationary before takeoff. If the plane travels 120 m from this point in 4 seconds, what is its speed at the point of takeoff?

The curve C is given by the equation $y = 2x^3 - 3x^2 - 12x + 6$ . The values of $x$ at which stationary points occur are

The curve C has the equation $y = f(x)$ . C has a stationary point at $(-2, 5)$ . If $f''(x) = x^4 - 15$ , then $(-2, 5)$ is

a minimum turning point

a maximum turning point

If $f(x) = \sin 3x - \cos 4x$ , then $f''(x) =$

9 sin 3x - 16 cos 4x

9 sin 3x + 16 cos 4x

-9 sin 3x + 16 cos 4x

Given an expression for the acceleration of a moving object, the velocity of the object can be found by

squaring the expression

integrating the expression

differentiating the expression

square rooting the expression

If $X = \int_{a}^{b} f(x)dx$ and $a < c < b$ , then $X=$

$\int_{a}^{c} f(x)dx + \int_{c}^{b} f(x)dx$

If $c$ is a constant, then $\int (2x-5)^3 dx=$

$\frac{(2x-5)^4}{4} + c$

$\frac{(2x-5)^2}{8} + c$

$\frac{(2x-5)^4}{8} + c$

$\frac{2(2x-5)}{4} + c$

If $c$ is a constant, then $\int (\sin x + 2 \cos x) dx=$

2 $\sin x - \cos x + c$

$\cos x + 2 \sin x + c$

$\cos x - 2 \sin x + c$

2 $\sin x + \cos x + c$

The region R is enclosed by the x-axis, the curve $y = -x^2 + 2$ and the lines $x = 0$ and $x=1$ . The area of R is

There are 108 cards in a deck of UNO playing cards. There are four "Wild", four "Wild Draw Four" and 25 each of four colours (red, yellow, green, blue). If a player needs to select 1 card, what is the probability of NOT drawing a "Wild Draw Four"?

Which of the following values describes the range of heights in the class?

The probability, expressed to two decimal places, of selecting a student who failed is

Items 44 and 45 refer to the following Venn diagram. There are 120 students in a school's music club. The Venn diagram shows the probabilities that a randomly selected student plays the piano (N) or guitar (G). X N G 0.40 0.35 0.15

What is the value of X?

$\frac{x^2-6}{(x^2-9)(x+3)}$

$a=1 \quad h=-4 \quad k=3$

$a=-1 \quad h=4 \quad k=3$

$\frac{1}{2}(\sqrt{5}-3)$

$\frac{1}{3}(\sqrt{5}-3)$

$\frac{1}{2}(3-\sqrt{5})$

$3^{\frac{3m+1}{n}}$

$(-3, -1)$ and $(-1, -3)$

$(-3, -1)$ and $(1, 3)$

$\cos^{-1}\left(\frac{11}{\sqrt{290}}\right)$

$\cos^{-1}\left(\frac{\sqrt{11}}{\sqrt{290}}\right)$

$\cos^{-1}\left(\frac{-1}{\sqrt{290}}\right)$

$\sin x = -\frac{1}{3}$

$\cos x = -\frac{1}{3}$

$\frac{1}{\sqrt{5-x}}$

$\frac{1}{2\sqrt{5-x}}$

$-\frac{1}{2\sqrt{5-x}}$

$\int_{a}^{c} f(x)dx + \int_{a}^{b} f(x)dx$

$\int_{a}^{c} f(x)dx + \int_{c}^{b} f(x)dx$

$\int_{0}^{a} f(x)dx + \int_{0}^{c} f(x)dx - \int_{0}^{b} f(x)dx$

CSEC Additional Mathematics Paper 1 May/June 2022 - Free CXC Past Paper with Answers

CSEC Additional Mathematics Paper 1 May/June 2022 Questions