Daily Practice · Higher Plus
July 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2014y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 2nd July 2014In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 3rd July 2014The probability of winning a game is 5/8. A player expects 30 wins. How many games did they play?
- 4th July 2014On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th July 2014A car covers 400 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th July 2014A quadratic sequence starts 0, 11, 32, 63. Work out the second difference, and the coefficient of n^2.
- 7th July 2014y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 8th July 2014In a vector proof you find that vector PQ = 5a - 4b and vector RS = 20a - 16b. What does this show about PQ and RS?
- 9th July 2014A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 10th July 2014A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 11th July 2014Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 12th July 2014Solve x^2 + 5x - 6 < 0.
- 13th July 2014y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 36.
- 14th July 2014A cuboid measures 7 cm by 7 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th July 2014A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th July 2014On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th July 2014Simplify sqrt(18) + sqrt(32), giving your answer in the form a sqrt(b).
- 18th July 2014Write x^2 - 4x - 3 in the form (x + a)^2 + b.
- 19th July 2014A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 20th July 2014A cuboid measures 12 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st July 2014A bag holds 3 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd July 2014A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 23rd July 2014A rectangle is 26 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th July 2014Work out the coordinates of the turning point of y = x^2 + 8x + 2.
- 25th July 2014y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 26th July 2014The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 27th July 2014A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 28th July 2014On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th July 2014Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 30th July 2014Simplify (x^2 - x - 2)/(x - 2).
- 31st July 2014y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.