Daily Practice · Higher Plus
June 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2004 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2004A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 2nd June 2004On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd June 2004Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 4th June 2004f(x) = 2x + 1 and g(x) = 6x - 1. Work out fg(-1).
- 5th June 2004A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 6th June 2004A cuboid measures 8 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th June 2004A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th June 2004A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 9th June 2004A rectangle is 25 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th June 2004The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 11th June 2004y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 12th June 2004A cuboid measures 10 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th June 2004A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th June 2004On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th June 2004Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 16th June 2004A quadratic sequence starts 10, 28, 56, 94. Work out the second difference, and the coefficient of n^2.
- 17th June 2004y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 18th June 2004The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 19th June 2004A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 20th June 2004A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 21st June 2004A block has mass 500 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.
- 22nd June 2004Solve x^2 + 13x + 40 > 0.
- 23rd June 2004y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 16.
- 24th June 2004In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 25th June 2004The probability of winning a game is 1/2. A player expects 60 wins. How many games did they play?
- 26th June 2004On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th June 2004x = 140 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th June 2004Write x^2 + 14x + 10 in the form (x + a)^2 + b.
- 29th June 2004A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 30th June 2004In a vector proof you find that vector PQ = 4a + 3b and vector RS = 20a + 15b. What does this show about PQ and RS?