Daily Practice · Higher Plus
September 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2009 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2009y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 49.
- 2nd September 2009In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 3rd September 2009A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 4th September 2009On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th September 2009A car covers 570 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th September 2009Work out the nth term of the quadratic sequence 7, 15, 29, 49, ...
- 7th September 2009A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 8th September 2009A cuboid measures 8 cm by 8 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th September 2009A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th September 2009A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 11th September 2009Rationalise the denominator of 50/sqrt(5), giving your answer in its simplest form.
- 12th September 2009The point (-6, 3) lies on y = f(x). Write down its image on y = f(x) - 1.
- 13th September 2009y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 14th September 2009A cuboid measures 9 cm by 9 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th September 2009A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th September 2009On 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?
- 17th September 2009Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 18th September 2009Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 19th September 2009y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 20th September 2009The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 21st September 2009A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
- 22nd September 2009A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 23rd September 2009A rectangle is 10 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th September 2009f(x) = 2x - 3 and g(x) = 6x - 8. Work out fg(-1).
- 25th September 2009y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 16.
- 26th September 2009In 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.
- 27th September 2009The probability of winning a game is 4/5. A player expects 16 wins. How many games did they play?
- 28th September 2009On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th September 2009Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 30th September 2009The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.