Daily Practice · Higher Plus
June 1958 5-a-day
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The batch download puts all 5 tiers' June 1958 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1958y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 36.
- 2nd June 1958In a vector proof you find that vector PQ = 2a - 5b and vector RS = 8a - 20b. What does this show about PQ and RS?
- 3rd June 1958A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 4th June 1958On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th June 1958Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 6th June 1958Work out the coordinates of the turning point of y = x^2 + 4x - 15.
- 7th June 1958A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 8th June 1958A cuboid measures 5 cm by 13 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th June 1958A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th June 1958A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 11th June 1958A rectangle is 30 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th June 1958Simplify (x^2 - 4x + 3)/(x - 3).
- 13th June 1958y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 14th June 1958A cuboid measures 10 cm by 12 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th June 1958A bag holds 3 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th June 1958On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th June 1958Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 18th June 1958In an algebraic proof, how would you write an even number in terms of an integer n?
- 19th June 1958y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 20th June 1958The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 21st June 1958A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 22nd June 1958A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 23rd June 1958A block has mass 350 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th June 1958Make x the subject of 7x + 8 = y(x + 8).
- 25th June 1958y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 64.
- 26th June 1958In 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.
- 27th June 1958The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 28th June 1958On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th June 1958x = 189 and y = 83, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th June 1958Write 6/(x - 5) + 5/(x - 6) as a single fraction.