Practise questions | Salam Academy

SA-IAL-P1-AL-0152 marksL2 StandardCalculatorSketching

The curve

y=\dfrac{2}{x-3}

has asymptotes

x=a

and

y=b

. Write down

a

and

b

.

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SA-IAL-P1-AL1-0023 marksL2 StandardNon-calculatorIndices

Solve

3^{2x-1}=27

.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0044 marksL2 StandardNon-calculatorEquations & inequalities

Solve the simultaneous equations

y=2x

and

y=x^2-3

. Give the two values of

x

.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-DF-0063 marksL2 StandardCalculatorGradients

Find the

x

-coordinates of the points on

y=x^3-3x^2

where the gradient is

9

.

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SA-IAL-P1-DF-0074 marksL2 StandardCalculatorTangents

Find the equation of the tangent to

y=x^2-4x+1

at the point where

x=3

, in the form

y=mx+c

.

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SA-IAL-P1-DF-0084 marksL2 StandardCalculatorNormals

Find the equation of the normal to

y=\dfrac8x

at the point where

x=2

, in the form

y=mx+c

.

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SA-IAL-P1-DF2-0063 marksL2 StandardNon-calculatorGradients

The curve

y=x^3+kx

has gradient

7

at

x=1

. Find

k

.

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SA-IAL-P1-DF3-0033 marksL2 StandardNon-calculatorNormals

Find the equation of the normal to

y=x^2

at

(1,1)

, in the form

y=mx+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-IN-0044 marksL2 StandardCalculatorFinding the curve

f'(x)=6x-4

, and the curve

y=f(x)

passes through

(1,5)

. Find

f(x)

.

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SA-IAL-P1-IN-0082 marksL2 StandardCalculatorPower rule

Find

\displaystyle\int5x^{\frac23}\,dx

.

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SA-IAL-P1-IN2-0023 marksL2 StandardNon-calculatorApplying it

f'(x)=3x^2

and

f(0)=-2

. Find

f(2)

.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-TR-0023 marksL2 StandardCalculatorSine & cosine rules

A triangle has sides

5

cm,

6

cm and

8

cm. Find the largest angle, in degrees to 1 decimal place.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-TR1-0023 marksL2 StandardCalculatorSine & cosine rules

In triangle

ABC

,

a=6

cm,

b=8

cm and angle

A=30^\circ

. Angle

B

is acute. Find

B

, in degrees to 1 decimal place.

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S1-CR-0034 marksL2 StandardCalculatorRegression line

For

8

pairs of values,

\sum x=48

,

\sum y=120

,

S_{xx}=32

and

S_{xy}=40

. The regression line of

y

on

x

is

y=a+bx

. Find

b

and

a

.

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SA-IAL-S1-CR-0043 marksL2 StandardCalculatorUsing the line

The regression line

y=7.5+1.25x

was found from data with

x

between

2

and

10

. (i) Estimate

y

when

x=7

. (ii) Which estimate would be unreliable?

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-S1-DR-0014 marksL2 StandardCalculatorE and Var

X

takes the values

1

,

2

,

3

with probabilities

0.2

,

0.5

,

0.3

. Find (i)

E(X)

and (ii)

\text{Var}(X)

.

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SA-IAL-S1-DR-0083 marksL2 StandardCalculatorE and Var

E(X)=3

and

E(X^2)=11

. Find (i)

\text{Var}(X)

and (ii)

\text{Var}(2X+5)

.

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SA-IAL-S1-DR1-0052 marksL2 StandardNon-calculatorProbability function

P(X=x)=\dfrac x{15}

for

x=1,2,3,4,5

. Find

P(X>3)

.

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SA-IAL-S2-CD-0084 marksL2 StandardCalculatorNormal approximations

X\sim\text{Po}(25)

. Use a normal approximation to find

P(X>30)

, correct to 3 significant figures.

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SA-IAL-S2-CD2-0024 marksL2 StandardCalculatorNormal approximations

X\sim\text{Po}(50)

. Use a normal approximation to find

P(X\le45)

, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

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