Daily Practice · Higher Plus
June 1971 5-a-day
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The batch download puts all 5 tiers' June 1971 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1971A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd June 1971A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 3rd June 1971Simplify sqrt(48) + sqrt(3), giving your answer in the form a sqrt(b).
- 4th June 1971Work out the nth term of the quadratic sequence 7, 18, 33, 52, ...
- 5th June 1971y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 49.
- 6th June 1971A cuboid measures 11 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th June 1971A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th June 1971On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th June 1971A rectangle is 8 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th June 1971The point (2, -6) lies on y = f(x). Write down its image on y = f(x + 1).
- 11th June 1971A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
- 12th June 1971The 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.
- 13th June 1971A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 14th June 1971A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 15th June 1971Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 16th June 1971Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 17th June 1971y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 18th June 1971In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 19th June 1971The probability of winning a game is 3/5. A player expects 39 wins. How many games did they play?
- 20th June 1971On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st June 1971A block has mass 770 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd June 1971f(x) = 5x + 5 and g(x) = 4x + 1. Work out fg(-3).
- 23rd June 1971y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 24th June 1971In a vector proof you find that vector PQ = a + 4b and vector RS = 4a + 16b. What does this show about PQ and RS?
- 25th June 1971A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 26th June 1971A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 27th June 1971x = 44 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th June 1971The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 29th June 1971y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 4.
- 30th June 1971A cuboid measures 13 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.