Daily Practice · Higher Plus
June 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2014 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2014A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd June 2014In 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.
- 3rd June 2014The probability of winning a game is 3/5. A player expects 42 wins. How many games did they play?
- 4th June 2014A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 5th June 2014Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 6th June 2014Work out the nth term of the quadratic sequence -5, 1, 13, 31, ...
- 7th June 2014y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 8th June 2014In a vector proof you find that vector PQ = 2a + 2b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 9th June 2014A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 10th June 2014On 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?
- 11th June 2014A rectangle is 16 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th June 2014The point (3, -6) lies on y = f(x). Write down its image on y = -f(x).
- 13th June 2014y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 14th June 2014A cuboid measures 15 cm by 10 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th June 2014A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th June 2014A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 17th June 2014Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 18th June 2014Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 19th June 2014y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 4.
- 20th June 2014A cuboid measures 14 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st June 2014A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd June 2014On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd June 2014A block has mass 260 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th June 2014f(x) = 2x - 7 and g(x) = 5x + 7. Work out fg(-3).
- 25th June 2014A train slows steadily from 20 m/s to rest in 8 seconds. Work out its deceleration.
- 26th June 2014The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 27th June 2014A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 28th June 2014A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 29th June 2014x = 184 and y = 111, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th June 2014The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.