Daily Practice · Higher Plus
August 1969 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1969 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1969Write x^2 - 6x - 7 in the form (x + a)^2 + b.
- 2nd August 1969y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 4.
- 3rd August 1969In a vector proof you find that vector PQ = 6a + 6b and vector RS = 24a + 24b. What does this show about PQ and RS?
- 4th August 1969A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th August 1969On 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?
- 6th August 1969A rectangle is 20 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th August 1969Work out the coordinates of the turning point of y = x^2 + 4x - 6.
- 8th August 1969A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 9th August 1969A cuboid measures 5 cm by 3 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th August 1969A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th August 1969A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 12th August 1969Expand and simplify (9 + sqrt(2))(9 - sqrt(2)).
- 13th August 1969Simplify (x^2 + 9x + 8)/(x + 8).
- 14th August 1969y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 15th August 1969A cuboid measures 11 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th August 1969A 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?
- 17th August 1969On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th August 1969A block has mass 750 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th August 1969In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 20th August 1969y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 21st August 1969The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 22nd August 1969A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 23rd August 1969A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 24th August 1969x = 161 and y = 83, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th August 1969Make x the subject of 6x + 3 = y(x + 3).
- 26th August 1969y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 4.
- 27th August 1969In 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.
- 28th August 1969The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 29th August 1969On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th August 1969A car covers 620 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st August 1969Write 3/(x - 4) + 6/(x + 3) as a single fraction.