A-Level Mathematics Revision

What are the asymptotes of the graph 

of  $y=\frac{3x-19}{x-2}$  ?

• x = 2 and y = 19

• x = -2 and y = 3

• x = 2 and y = 3

• x = -2 and y = 3x

Consider the graph below defined by the equation

3ln(x) +6xy – 3y² = 18

Describe the relationship between x and y if a tangent to the curve is vertical.

• y = 2x

• y = 18x

• y = 3

• y = x

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

Solve  $\left|\left(x-3\right)\left(x+2\right)\right|\ <x-1$  

• -1.45 < x < 2.65

• 2.65 < x < 3.45

• x < 2.65 or x > 3.45

• never

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve:  $\log_2\left(x+1\right)\ =\ 3\ +\ \log_2\left(x-2\right)$  

•  $\frac{17}{7}$  

•  $\frac{7}{17}$  

•  $\frac{19}{9}$  

•  $\frac{19}{7}$  

Tags

CCSS.HSF.BF.B.5

When x = 1, what is the equation of the tangent to the curve defined parametrically as x = 2T - 3, y = (T + 1)³?

• $y=\frac{27}{2x}+\frac{27}{2}$

• $y=\frac{27}{2}x-\frac{27}{2}$

• $2y-27x=27$

• $27y-2x=27$

 $\cos\left(3\theta\right)=4\cos^3\left(\theta\right)-3\cos\left(\theta\right)$  Use this result to find the exact value of  $\int_{\frac{\pi}{3}}^{\frac{\pi}{2}}\cos^3\left(\theta\right)d\theta$  

•  $\frac{2}{3}$  

•  $\sqrt{3}$  

•  $\frac{2}{3}+\frac{3}{8}\sqrt{3}$  

•  $\frac{2}{3}-\frac{3}{8}\sqrt{3}$  

Convert -4 - 3i into polar form.

• 5 cis 2.498

• 5 cis -0.644

• 5 cis 3.786

• 5 cis -2.498

Tags

CCSS.HSN.CN.B.4

CCSS.HSN.CN.B.5

Solve the equation $\sin\left(x\right)=\frac{3}{4}\pi-x$  using a numerical method, to 3dp.

• 1.375

• 1.376

• 1.378

• 1.379

Tags

CCSS.HSA.REI.D.11

CCSS.HSF.IF.C.7

CCSS.HSF.TF.B.7

 u = 13cis1.14 (radians) and v = 3 + 4i. Evaluate  $\left|u+v\right|$  

• 65cis(2.07)

• 65

• 8.43 + 15.8i

• 17.92

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

CCSS.HSN.CN.B.4

CCSS.HSN.CN.B.5

A line has an equation of R = i + 2j + k + T(2i - j + k). A plane p has equation ax + y + z = 5, where a is a constant. The acute angle between the line and the plane is 0.730 (3sf). Find the value(s) of a.

•  $\pm1$  

•  $\pm4$  

•  $\pm2$  

•  $\pm3$  

Tags

CCSS.HSG.GPE.B.5

CCSS.HSN.VM.A.1