Daily Practice · Higher Plus
July 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2024The point (-3, 3) lies on y = f(x). Write down its image on y = f(x) - 5.
- 2nd July 2024y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 3rd July 2024The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 4th July 2024A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 5th July 2024A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 6th July 2024A car covers 440 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th July 2024Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 8th July 2024y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 64.
- 9th July 2024In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 10th July 2024The probability of winning a game is 1/5. A player expects 16 wins. How many games did they play?
- 11th July 2024On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th July 2024Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 13th July 2024f(x) = 5x - 6 and g(x) = 4x + 3. Work out fg(4).
- 14th July 2024A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 15th July 2024In a vector proof you find that vector PQ = a - 3b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 16th July 2024A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 17th July 2024A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 18th July 2024Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 19th July 2024The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 20th July 2024y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 21st July 2024A cuboid measures 6 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd July 2024A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd July 2024On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th July 2024A rectangle is 10 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th July 2024A quadratic sequence starts 13, 19, 27, 37. Work out the second difference, and the coefficient of n^2.
- 26th July 2024y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 27th July 2024A cuboid measures 13 cm by 13 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th July 2024A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th July 2024A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 30th July 2024Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 31st July 2024Solve x^2 + 10x + 21 > 0.