Salam Academy
Sign inCreate account
Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

Sign in to check answers. Your attempts build your mastery and error book.

2730 questions · page 91 of 137 · choose a topic above to narrow them down

SA-9709-P5-DV4-0022 marksL2 StandardCalculatorGeometric
A fair die is thrown until a six appears. Find the probability that a six appears within the first 33 throws, as a fraction.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-DV4-0052 marksL2 StandardCalculatorGeometric
X∼Geo(0.4)X\sim\text{Geo}(0.4). Find P(X≥3)P(X\ge3).

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-ND-0033 marksL2 StandardCalculatorInverse normal
X∼N(100,152)X\sim N(100,15^2). Find the value of kk such that P(X<k)=0.9P(X<k)=0.9, correct to 1 decimal place.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-ND-0043 marksL2 StandardCalculatorInverse normal
X∼N(100,152)X\sim N(100,15^2). Find kk such that P(X>k)=0.05P(X>k)=0.05, correct to 1 decimal place.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-ND2-0023 marksL2 StandardCalculatorInverse normal
X∼N(80,100)X\sim N(80,100). Find kk such that P(X>k)=0.2P(X>k)=0.2, correct to 3 significant figures.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-ND2-0073 marksL2 StandardCalculatorInverse normal
Exam marks are normally distributed with mean 5555 and standard deviation 1212. The top 5%5\% of candidates receive an A*. Find the minimum mark for an A*, correct to 3 significant figures.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-ND3-0024 marksL2 StandardCalculatorApproximation
X∼B(80,0.5)X\sim B(80,0.5). Use a suitable normal approximation to find P(X≤35)P(X\le35), correct to 3 significant figures.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-ND3-0044 marksL2 StandardCalculatorApproximation
X∼B(200,0.3)X\sim B(200,0.3). Use a normal approximation to find P(X>70)P(X>70), correct to 3 significant figures.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-PC-0032 marksL2 StandardCalculatorTogether / apart
In how many arrangements of the letters of BANANA are the two Ns next to each other?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-PC-0053 marksL2 StandardCalculatorRestrictions
How many arrangements of the letters of ORANGE begin and end with a vowel?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-PC-0072 marksL2 StandardCalculatorSelections
A committee of 55 is chosen from 77 men and 55 women. How many committees contain exactly 22 women?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-PC2-0032 marksL2 StandardCalculatorTogether / apart
Six people stand in a line. In how many arrangements are A and B not next to each other?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-PC3-0052 marksL2 StandardCalculatorSelections
A committee of 55 is chosen from 1010 people, one of whom is Ali. How many committees include Ali?

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P5-PR-0053 marksL2 StandardCalculatorTree diagrams
From the same bag (55 red, 33 blue), two counters are taken without replacement. Find the probability that they are different colours.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0024 marksL2 StandardCalculatorE(X)
For f(x)=x29f(x)=\tfrac{x^2}9 on 0≤x≤30\le x\le3, find E(X)E(X) and Var(X)\text{Var}(X).

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0033 marksL2 StandardCalculatorMedian
For f(x)=x29f(x)=\tfrac{x^2}9 on 0≤x≤30\le x\le3, find the median, correct to 3 significant figures.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0044 marksL2 StandardCalculatorPDFs
f(x)=k(4−x)f(x)=k(4-x) for 0≤x≤40\le x\le4, and 00 otherwise. Find kk and P(X>1)P(X>1).

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR-0063 marksL2 StandardCalculatorPercentiles
f(x)=x2f(x)=\tfrac x2 for 0≤x≤20\le x\le2, and 00 otherwise. Find the upper quartile, giving an exact answer.

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0023 marksL2 StandardCalculatorVar(X)
For f(x)=x8f(x)=\tfrac x8 on 0≤x≤40\le x\le4 (with E(X)=83E(X)=\tfrac83), find Var(X)\text{Var}(X).

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme
SA-9709-P6-CR2-0043 marksL2 StandardCalculatorVar(X)
For f(x)=38x2f(x)=\tfrac38x^2 on 0≤x≤20\le x\le2, with E(X)=1.5E(X)=1.5, find Var(X)\text{Var}(X).

Sign in or create a free account to check answers, get hints and track your progress.

Salam Academy Original Practice · Proposed mark scheme