Daily Practice · Higher Plus
July 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2017A car covers 550 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.
- 2nd July 2017Work out the nth term of the quadratic sequence 8, 17, 34, 59, ...
- 3rd July 2017A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
- 4th July 2017A cuboid measures 7 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th July 2017A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th July 2017A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 7th July 2017Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.
- 8th July 2017The point (2, 6) lies on y = f(x). Write down its image on y = f(x) + 4.
- 9th July 2017y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 10th July 2017The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 11th July 2017A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 12th July 2017On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th July 2017Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 14th July 2017Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 15th July 2017y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 16th July 2017In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 17th July 2017The probability of winning a game is 4/5. A player expects 20 wins. How many games did they play?
- 18th July 2017A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 19th July 2017A rectangle is 29 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th July 2017f(x) = 4x - 9 and g(x) = 2x + 5. Work out fg(0).
- 21st July 2017y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 81.
- 22nd July 2017In a vector proof you find that vector PQ = a + 3b and vector RS = 3a + 9b. What does this show about PQ and RS?
- 23rd July 2017A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 24th July 2017On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th July 2017Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 26th July 2017The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 27th July 2017A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 28th July 2017A cuboid measures 15 cm by 3 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th July 2017A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th July 2017A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 31st July 2017A block has mass 780 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.