Daily Practice · Higher Plus
August 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1965A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd August 1965On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd August 1965Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 4th August 1965Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 5th August 1965A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 6th August 1965A cuboid measures 11 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th August 1965A bag holds 5 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th August 1965A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 9th August 1965A block has mass 410 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th August 1965f(x) = 3x - 5 and g(x) = 6x - 3. Work out fg(-1).
- 11th August 1965y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 12th August 1965The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 13th August 1965A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
- 14th August 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?
- 15th August 1965x = 66 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th August 1965The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 17th August 1965y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 18th August 1965In 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 August 1965The probability of winning a game is 3/4. A player expects 21 wins. How many games did they play?
- 20th August 1965A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 21st August 1965A car covers 720 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd August 1965A quadratic sequence starts 8, 20, 36, 56. Work out the second difference, and the coefficient of n^2.
- 23rd August 1965y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 36.
- 24th August 1965In a vector proof you find that vector PQ = 2a + 2b and vector RS = 4a + 4b. What does this show about PQ and RS?
- 25th August 1965A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 26th August 1965On 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?
- 27th August 1965Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 28th August 1965Solve x^2 + 12x + 35 > 0.
- 29th August 1965A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 30th August 1965A cuboid measures 3 cm by 7 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st August 1965A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?