Number · SS1

Number bases

Counting in bases other than ten (base 2, 5, 8 …), and converting and calculating between them.

Before this: Number foundations & fractions

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1Number basesPlace values as powers of the base, converting to and from base ten, changing between two other bases, arithmetic in a base, and finding an unknown base.Done22 min

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Answer number bases questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.

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Past questions (46)

From 1984–2025: 14 WAEC, 6 NECO, 26 JAMB. Theory questions first, then objective, newest first.

Theory (9)

NECO 2024 · Paper 2 · Q2The 4th and 7th terms of a geometric progression are 8 and $\frac{64}{27}$ respectively. Find the (i) common ratio; (ii) first term.
NECO 2024 · Paper 2 · Q6Use mathematical tables to evaluate $\dfrac{\sqrt[4]{4000} \times 75.9}{5.61 \times 4.39}$ .
NECO 2023 · Paper 2 · Q6If $135_k = 231_{\text{four}}$ , find the value of $k$ .
WAEC 2019 · Paper 2 · Q1Given that $110_x = 40_{\text{five}}$ , find the value of $x$ .
WAEC 2019 · Paper 2 · Q3Without using mathematical tables or a calculator, simplify $\dfrac{\log_2 8 + \log_2 16 - 4\log_2 2}{\log_4 16}$ .
WAEC 2018 · Paper 2 · Q4In the diagram, $QOS$ is a diameter, $\angle RQS = x^\circ$ and $\angle QST = (3x + 15)^\circ$ , where $RST$ is a straight line. Find: (i) the …
WAEC 2014 · Paper 2 · Q2Simplify $3\sqrt{75} - \sqrt{12} + \sqrt{108}$ , leaving the answer in surd form (radicals).
WAEC 2010 · Paper 2 · Q4Find the value of $x$ if $x3_{\text{five}} - 14_{\text{five}} = 2x_{\text{five}}$ .
WAEC 2009 · Paper 2 · Q6By how much is $11000_2$ greater than or less than $111_2 \times 11_2$ ? Give your answer in base two.

Objective (37)

WAEC 2025 · Paper 1 · Q1Find $(101_2)^2$ , expressing the answer in base 2.
NECO 2024 · Paper 1 · Q3Evaluate $3241_{\text{five}} - 1342_{\text{five}}$ .
WAEC 2024 · Paper 1 · Q27The number $1621$ was subtracted from $6244$ in base $x$ . If the result was $4323$ , find $x$ .
NECO 2023 · Paper 1 · Q2Find the product of $10110_{\text{two}}$ and $11_{\text{two}}$ .
WAEC 2023 · Paper 1 · Q19Arrange the following in ascending order of magnitude: $110_{\text{two}}$ , $31_{\text{eight}}$ , $42_{\text{five}}$ .
WAEC 2023 · Paper 1 · Q5Express $413_7$ in base 5.
NECO 2022 · Paper 1 · Q15Simplify $110011_{\text{two}} \times 101_{\text{two}}$ .
WAEC 2022 · Paper 1 · Q2Change $432_{\text{five}}$ to a number in base three.
WAEC 2021 · Paper 1 · Q2Simplify $(11_{\text{two}})^2$ .
WAEC 2020 · Paper 1 · Q6If $101_{\text{two}} + 12_y = 23_{\text{five}}$ , find the value of $y$ .
WAEC 2019 · Paper 1 · Q8If $23_y = 1111_{\text{two}}$ , find the value of $y$ .
JAMB 2018 · UTME · Q1Find $x$ and $y$ respectively in the subtraction below. $$\begin{array}{rcccc} & 4 & 2 & 4 & 3 \ - & 1 & 3 & x & 4 \ \hline & y & 3 & 4 & 4 …
JAMB 2018 · UTME · Q19Convert $241_5$ to base 8.
JAMB 2017 · UTME · Q10Find $x$ and $y$ respectively in the subtraction below, carried out in base 5. $$\begin{array}{rcccc} & 4 & 2 & 4 & 3 \ - & 1 & 3 & x & 4 \ …
JAMB 2017 · UTME (set 2) · Q16The addition below was carried out in a certain base. $\begin{array}{rr} & 1101.01 \\ + & 1110.11 \\ & 1011.10 \\ \hline & 100111.10 \end{array}$ …
JAMB 2015 · UTME · Q14Write the decimal number 39 in base 2.
JAMB 2013 · UTME · Q2Convert $27_{10}$ to a number in base three.
JAMB 2012 · UTME · Q2Convert $112_6$ to a number in base three.
JAMB 2011 · UTME · Q2If $2q3_5 = 77_8$ , find $q$ .
JAMB 2010 · UTME · Q2Find $r$ , if $6r7_8 = 511_9$ .
JAMB 2004 · UME · Q1Find $x$ and $y$ respectively in the subtraction below, carried out in base 5. $$\begin{array}{rcccc} & 4 & 2 & 4 & 3 \ - & 1 & 3 & x & 4 \ …
JAMB 2004 · UME · Q2Find $p$ if $451_6 - p_7 = 305_6$ .
JAMB 2003 · UME · Q3Simplify $213_4 \times 23_4$ .
JAMB 2003 · UME · Q6The sum of four numbers is $1214_5$ . What is the average expressed in base five?
JAMB 2000 · UME · Q10If $P344_6 - 23P2_6 = 2PP2_6$ , find the value of the digit $P$ .
JAMB 1999 · UME · Q5Divide $2434_6$ by $42_6$ .
JAMB 1998 · UME · Q1If $1011_2 + X_7 = 25_{10}$ , solve for $X$ .
JAMB 1997 · UME · Q1If $(1P03)_4 = 115_{10}$ , find $P$ .
JAMB 1995 · UME · Q1Calculate $3310_5 - 1442_5$ .
JAMB 1993 · UME · Q1Change $71_{10}$ to base 8.
JAMB 1992 · UME · Q1Find $n$ if $34_n = 10011_2$ .
JAMB 1991 · UME · Q2If 2257 is the result of subtracting 4577 from 7056 in base $n$ , find $n$ .
JAMB 1987 · UME · Q1Convert $241_5$ to base 8.
JAMB 1986 · UME · Q1Evaluate $212_3 - 121_3 + 222_3$ .
JAMB 1985 · UME · Q3In the equation $\dfrac{11}{x} = \dfrac{1000}{x + 101}$ , all the numbers are in base 2. Solve for $x$ .
JAMB 1984 · UME · Q12A trader in a country whose currency, the Mont (M), is in base five bought $103_5$ oranges at $M14_5$ each. If he sold the oranges at $M24_5$ …
JAMB 1984 · UME · Q2If $263 + 441 = 714$ , what number base has been used?