Daily Practice · Higher Plus
June 1961 5-a-day
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The batch download puts all 5 tiers' June 1961 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1961Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 2nd June 1961f(x) = 5x + 6 and g(x) = 4x - 4. Work out fg(0).
- 3rd June 1961y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 4th June 1961The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 5th June 1961A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 6th June 1961A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 7th June 1961A rectangle is 9 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th June 1961The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 9th June 1961y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 64.
- 10th June 1961In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 11th June 1961The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 12th June 1961On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th June 1961Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 14th June 1961A quadratic sequence starts 2, 11, 28, 53. Work out the second difference, and the coefficient of n^2.
- 15th June 1961A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 16th June 1961In a vector proof you find that vector PQ = a + 5b and vector RS = 4a + 20b. What does this show about PQ and RS?
- 17th June 1961A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 18th June 1961A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 19th June 1961A block has mass 550 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th June 1961Solve x^2 - 16 < 0.
- 21st June 1961y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 22nd June 1961A cuboid measures 4 cm by 14 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd June 1961A 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?
- 24th June 1961On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th June 1961x = 170 and y = 158, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th June 1961Write x^2 - 16x - 14 in the form (x + a)^2 + b.
- 27th June 1961y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 28th June 1961A cuboid measures 4 cm by 11 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th June 1961A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th June 1961A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?