Daily Practice · Higher Plus
June 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1965 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1965A cuboid measures 5 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd June 1965A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd June 1965On 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?
- 4th June 1965Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 5th June 1965Simplify (x^2 - 3x + 2)/(x - 2).
- 6th June 1965y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 7th June 1965A cuboid measures 12 cm by 10 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th June 1965A bag holds 4 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th June 1965A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 10th June 1965Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 11th June 1965In an algebraic proof, how would you write a multiple of 5 in terms of an integer n?
- 12th June 1965y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 49.
- 13th June 1965The 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.
- 14th June 1965A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 15th June 1965On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th June 1965A rectangle is 29 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th June 1965Make x the subject of 4x + 5 = y(x + 5).
- 18th June 1965A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 19th June 1965In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 20th June 1965The probability of winning a game is 1/5. A player expects 7 wins. How many games did they play?
- 21st June 1965A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 22nd June 1965Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 23rd June 1965Write 2/(x - 1) + 2/(x - 6) as a single fraction.
- 24th June 1965y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 25th June 1965In a vector proof you find that vector PQ = 3a + 3b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 26th June 1965A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th June 1965On 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?
- 28th June 1965A block has mass 580 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th June 1965Solve 8x^2 + 10x + 3 = 0.
- 30th June 1965y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.