Question 1

Which of the following statements about the sum of the angles in a triangle is correct?

Accepted Answer

The sum of the angles in a triangle is always $$180^\circ.$$

Question 2

Given the quadratic equation $$2x^2 + x - 3 = 0$, which of the following is a correct solution for x$?

Accepted Answer

$$x = -1.618$$

Question 3

Which of the following is the correct factorisation of $$x^2$$ - $$y^2$$?

Accepted Answer

$$(x - y)(x + y)$$

Question 4

If $$P(x) = 2x^3$ + ax^2$ + bx + 9 is $$divided by $$(x - 2)$$ and the remainder is $$-6$$, what is the value of $$a$$ when $$P(x) is $$also divided by $$(x + 2)$$ and the remainder is $$1$$?

Accepted Answer

$$a = -10$$

Question 5

Which of the following is a correct application of the factor theorem?

Accepted Answer

If $$P(a) = 0$$, then $$(x - a) is a $$factor of $$P(x).$$

Question 6

A student claims that any quadrilateral with equal sides is a square. Which of the following is a valid counter-example?

Accepted Answer

A rhombus

Question 7

Solve for $$x in $$the equation $$\sin x = 0.453$$ for $$0^\circ \leq x \u003c 360^\circ.$$

Accepted Answer

$$x = 269^\circ or$$ $$x = 91^\circ$$

Question 8

Which of the following is the correct expansion for $$(x + y)^2$?

Accepted Answer

$$x^2 + 2xy$$ + $$y^2$$

Question 9

If $$	an x = 1.56$$, what are the possible values of $$x$$ for $$0^\circ \u003c x \u003c 360^\circ$$?

Accepted Answer

$$x = 57.3^\circ or$$ $$x = 237.3^\circ$$

Question 10

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic series with first term $$a$$ and common difference $$d$$?

Accepted Answer

$$S_n = \dfrac{n}{2}(2a + (n-1)d)$$

Question 11

A polynomial $$P(x)$$ has roots at $$x = -\frac{1}{2}$$ and $$x = 3. $$Which of the following is a possible quadratic factor of $$P(x)$$?

Accepted Answer

$$2x^2 + x - 3$

Question 12

Which of the following is the correct formula for the sum of the first $$n$$ terms of a geometric series with first term $$a$$ and common ratio $$r$$ ($$r 
eq 1$$)?

Accepted Answer

$$S_n = a \dfrac{1 - r^n}{1 - r}$$

Question 13

Which of the following is the correct expression for the difference of two squares?

Accepted Answer

$$x^2$$ - $$y^2 = (x - y)(x + y$$)$$

Question 14

If $$\cos x = 0.769$$, what are the possible values of $$x$$ for $$0^\circ \u003c x \u003c 360^\circ$$?

Accepted Answer

$$x = 140.3^\circ or$$ $$x = 219.7^\circ$$

Question 15

Which of the following is the correct result for $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 16

Which of the following is the correct formula for the $$nth $$term of an arithmetic sequence with first term $$a$$ and common difference $$d$$?

Accepted Answer

$$a_n = a + (n-1)d$$

Question 17

Which of the following is the correct formula for the $$nth $$term of a geometric sequence with first term $$a$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a r$$^{n-1}$$

Question 18

Which of the following is the correct binomial expansion for $$(1 + x)^3$?

Accepted Answer

$$1 + 3x + 3x^2$ + x^3$

Edexcel IAL Pure Mathematics 2: Revision Notes (Calculus and Related Topics)

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