Daily Practice · Higher Plus
January 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2024On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 2nd January 2024Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 3rd January 2024A quadratic sequence starts 11, 24, 43, 68. Work out the second difference, and the coefficient of n^2.
- 4th January 2024A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 5th January 2024The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 6th January 2024A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 7th January 2024A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 8th January 2024A block has mass 490 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th January 2024Solve x^2 - 10x + 21 > 0.
- 10th January 2024y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 11th January 2024In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 12th January 2024The probability of winning a game is 2/5. A player expects 30 wins. How many games did they play?
- 13th January 2024On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 14th January 2024x = 168 and y = 153, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th January 2024Write x^2 + 4x + 2 in the form (x + a)^2 + b.
- 16th January 2024y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 17th January 2024In a vector proof you find that vector PQ = a + 3b and vector RS = 5a + 15b. What does this show about PQ and RS?
- 18th January 2024A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 19th January 2024A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 20th January 2024A car covers 340 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st January 2024Work out the coordinates of the turning point of y = x^2 - 2x - 10.
- 22nd January 2024y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 49.
- 23rd January 2024A cuboid measures 11 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th January 2024A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th January 2024On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th January 2024Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 27th January 2024Simplify (x^2 + 2x - 48)/(x - 6).
- 28th January 2024A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 29th January 2024A cuboid measures 8 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th January 2024A bag holds 4 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st January 2024A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?